To say, "That Bicycle is mine" is very similar to your second example.

The particle "wa" is probably one of the more key parts of the expression, rather than a token particle.

Your second example says: "Sore wa watashi no jitensha desu."
Which when translated into English ideomatics, would be "That bike is mine." As will be explained after this, it literally means some to the lines of, "As for that, it is my bike."

"Wa" is commonly thought of as solely a "topic marker." In essence this is true. But it is the theme of the overall thought. So the sentence, "Sore wa watashi no jitensha desu" would say something to the tone of, "As for that, It is my bike.", as stated earlier. To say something a little more literal when translated English, it would be best to say "Sono jiensha wa watashi no desu." (As for that bike, it is mine. OR: That Bike is mine.) Its best not to be repetitive and say "jitensu" twice, unless you want to be totally correct.

As for the phrase, "That is mine.", you could say, "Sore wa watashi no desu." (As for that, it is mine.) Glad to be of service in any.

Gambatte kudasai.

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Nemuritai...

The pleasure of a dream is in its fantasy. If it ever comes true, it was never a dream.

My Genki textbook has said that "no" is a very versatile particle. I thought that it had to be used (for possesion) has an: object "no" object... Watashi (no) hon - my book..... nihongo (no) gakusee.... japanese student.

Watashi no desu... is an object "no" VERB... which isn't done in eigo. (And i know to learn a language NEVER compare it to your own.)

Since this is a new concept to me can someone further explan this to me.